Analysis 2
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Analysis 2: (Springer-Lehrbuch)

Analysis 2: (Springer-Lehrbuch)


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About the Book

Der zweite Band dieses Lehrbuchs der Analysis umfaßt den Stoff des zweiten Semesters eines mathematischen Grundstudiums für Studierende der Mathematik, Physik und Informatik. Der klare und übersichtliche Aufbau berücksichtigt, daß schon frühzeitig die mathematischen Hilfsmittel erörtert werden, die zum Verständnis der physikalischen Grundvorlesungen unerläßlich sind. In Verbindung mit Band 1 ist so ein Leitfaden für das Studium der Analysis entstanden, der das in den ersten beiden Studiensemestern zu erwerbende mathematische Grundwissen umfaßt. Ausführliche Beweise und Erläuterungen sowie zahlreiche Beispiele und interessante Übungsaufgaben eignen es sehr gut für das Selbststudium. Ein klarer und übersichtlicher Aufbau und eine geschickte Gliederung des Stoffes ermöglichen, das erste Studium auf Kernbereiche zu beschränken. Geometrische Intuition und historische Motivation in Verbindung mit einer maßvollen Abstraktion kennzeichnen diese moderne Einführung in die Analysis.

Table of Contents:
1 Differentialrechnung für Funktionen mehrerer Variabler.- 1 Partielle Ableitungen von Funktionen mehrerer Variabler.- 2 Differenzierbarkeit. Differential. Tangentialebene.- 3 Parameterabhängige Integrale.- 4 Differenzierbar keit parameterabhängiger uneigentlicher Integrale.- 5 Partielle Ableitungen höherer Ordnung.- 6 Taylorformel für Funktionen mehrerer Variabler.- 7 Lokale Extrema.- 8 Konvexe Mengen und konvexe Funktionen.- 9 Invertierbare Abbildungen.- 10 Legendretransformation.- 11 Satz von Heine-Borel. Lipschitzstetigkeit. Nullmengen.- 2 Kurven und Kurvenintegrale.- 1 Bogenlänge. Kurven- und Wegintegrale.- 2 Krümmung und Windung. Frenetsche Formeln.- 3 Das Anfangswertproblem III.- 4 Eindimensionale Variationsrechnung.- 3 Holomorphe Funktionen, Residuen, Fouriertransformation.- 1 Holomorphe Funktionen.- 2 Cauchys Integralformel.- 3 Potenzreihen und holomorphe Funktionen.- 4 Gebietstreue, Maximumprinzip, Schwarzsches Lemma.- 5 Nullstellen holomorpher Funktionen. Sätze von Hurwitz und Rouché.- 6 Abelscher Grenzwertsatz. Satz von Tauber.- 7 Isolierte Singularitäten. Laurentreihen. Meromorphe Funktionen.- 8 Berechnung uneigentlicher Integrale mit dem Residuensatz.- 9 Das Fouriersche Integral.- 10 Die Fouriertransformation auf dem Schwartzschen Räume S.- 4 Gleichungsdefinierte Mannigfaltigkeiten.- 1 Satz über implizite Funktionen. Mannigfaltigkeiten im ?n.- 2 Der Tangentialraum einer Mannigfaltigkeit.- 3 Extrema mit Nebenbedingungen. Lagrangesche Multiplikatoren.- 4 Enveloppen.- 5 Differentialgleichungen auf Mannigfaltigkeiten.- 6 Abstandsfunktion und Eikonalgleichung.- 5 Integralrechnung im ?n.- 1 Quadrierbare Mengen, Inhalt und Integral im ?n.- 2 Der Transformationssatz.- 3 Parameterabhängige Integrale. Eulersche Differentialgleichung.- 4Uneigentliche Integrale im ?n. Newtonsches Potential.- 6 Flächenintegrale und Integralsätze.- 1 Flächeninhalt.- 2 Flächenintegrale.- 3 Die Integralsätze von Gau? und Green.- 4 Satz von Stokes.

Review :
From the reviews: "This is the second volume of a proposed three volume series covering the analysis needs of students in mathematics, physics and computer science. ... The present volume is aimed at second semester students at German universities ... . The many applications are all of interest and all given a very thorough treatment, each chapter contains several sets of exercises and historical notes abound. Outside Germany this book should be on library shelves and would be of interest to all involved in the teaching of analysis." (Peter S. Bullen, Zentralblatt MATH, Vol. 1112 (8), 2007)


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Product Details
  • ISBN-13: 9783540439707
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • No of Pages: 514
  • Returnable: N
  • Width: 155 mm
  • ISBN-10: 3540439706
  • Publisher Date: 10 Mar 2003
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Series Title: Springer-Lehrbuch


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